The Kerr congruence

We present the special relativistic Kerr congruence from two new points of view. The importance of the Kerr congruence stems from its role in the general relativistic rotating body problem. In the special relativistic limit, it is the simplest twisting generalization of the ordinary light cone. We first show that the Kerr congruence can be obtained from the light cone of complex Minkowski space, which induces a family of oblate spheroids in real Minkowski space. We then show that the rigid rotation of one of these spheroids with constant angular velocity also generates the Kerr congruence by shining comoving flashlights normal to the surface. In fact, the oblate spheroid is the unique surface which generates a shear-free twisting null congruence in this manner. This result has direct generalization to the full Kerr geometry.